Parking lots will probably be pretty full at $20, especially with the red line shutdown next season.

The Red Line is not being shut down, it is merely being rerouted over the Green Line tracks. For anyone who catches the Red Line north of Cermak/Chinatown (which I would say is the vast majority of people who ride the L to the park) nothing is changing for you save for an extra 2 blocks you will need to walk to and fro.